Phi 8 Logic Pt 03 Syllogism Validity & Soundness

In the third lecture, we consider three distinct types of syllogism: disjunctive, conditional, and categorical. The conditional syllogism provides useful grounds to explore what is the single most important, as well as the single most difficult, concept in deductive logic: validity. We consider validity (of form) in contrast to truth-value (of content), and how they may coordinate to yield soundness of argument. In logic, “validity” is a term of art (one that does not correspond to the ordinary, dictionary definition) and so is counter-intuitive; thus one must make an effort to understand it, and to avoid common misconceptions. Above all in analyzing a deductive argument we must train ourselves to consider (formal) validity first, (substantive) truth or content second. Counter-intuitively, it turns out that sometimes valid forms can yield false conclusions; sometimes invalid forms can have true premises and even true conclusions; and so on. The one thing that can never happen is that a valid form, when coupled with true premises, can yield a false conclusion. That may seem like a small thing, but it is the very power of deductive reasoning and validity. The definition of validity also yields a straightforward pragmatic test, and from this we shall apply “substitution instances” as a universal test for deductive validity. Finally, we shall come back to the history of logic and consider Popper’s startling claims that induction is not really a separate type of logic at all, but turns out rather to be an instance of deduction, and a known bad form of deduction to boot.

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